ALL FILES NEEDED TO ANSWER THE QUESTIONS WILL BE POSTED AT THE BOTTOM

1a) Download a file named utilities.py to your folder and create a python file named mybayes.py. Import the following package. Note that utilities need to import matplotlib that may need the administrator privilege for installation. If it causes a problem, simply comment this import line.

import numpy as np

#import matplotlib.pyplot as plt

from sklearn.naive_bayes import GaussianNB

from sklearn import model_selection

#from utilities import visualize_classifier

1b) Download multivar_data_nb.txt as the data set. This file contains comma separated values in each line. Use numpys loadtxt function to read the data set. Add the following lines. Show the below printout and explain the meanings of X and y.

input_file = 'multivar_data_nb.txt'

data = np.loadtxt(input_file, delimiter=',')

X, y = data[:, :-1], data[:, -1]

print(X[:2,:])

print(y[:2])

1c) Open multivar_data_nb.txt that contains comma-separated values in each line. The last value is class. Look at the file and tell how many classes in the file?

1d) Add the following lines to the same python file. In Gaussian Nave Bayes classifier, the values associated in each class are expected to follow a Gaussian distribution. Please indicate the role of each line below.

http://scikit-learn.org/stable/modules/generated/sklearn.naive_bayes.GaussianNB.html

classifier = GaussianNB()

classifier.fit(X, y)

y_pred = classifier.predict(X)

1e) Add the following lines to the same python file. Run the python file and show the printout.

accuracy = 100.0 * (y == y_pred).sum() / X.shape[0]

print("Accuracy of Naive Bayes classifier =", round(accuracy, 2), "%")

1f) Please explain how the first line works above? Is it same as the equation we have learned in the class?

2a) Add the following lines to the same python file. Run the python file and indicate (1) what are the return values of the first line? (2) what are the meanings of the parameters, test_size and random_state?

http://scikit-learn.org/stable/modules/generated/sklearn.model_selection.train_test_split.html

X_train, X_test, y_train, y_test = model_selection.train_test_split(X, y, test_size=0.2, random_state=3)

classifier_new = GaussianNB()

classifier_new.fit(X_train, y_train)

y_test_pred = classifier_new.predict(X_test)

2b) Compare y_test_pred = classifier_new.predict(X_test) with y_pred = classifier.predict(X). Please indicate which one is more objective to evaluate AI systems performance? Explain why?

2c) Add the following lines to the same python file. Run the file and show the printout below.

accuracy = 100.0 * (y_test == y_test_pred).sum() / X_test.shape[0]

print("Accuracy of the new classifier =", round(accuracy, 2), "%")

2d) Add the following lines to the same python file. Run the file and show the printout below.

num_folds = 3

accuracy_values = model_selection.cross_val_score(classifier, X, y, scoring='accuracy', cv=num_folds)

print("Accuracy: " + str(round(100*accuracy_values.mean(), 2)) + "%")

precision_values = model_selection.cross_val_score(classifier, X, y, scoring='precision_weighted', cv=num_folds)

print("Precision: " + str(round(100*precision_values.mean(), 2)) + "%")

f1_values = model_selection.cross_val_score(classifier, X, y, scoring='f1_weighted', cv=num_folds)

print("F1: " + str(round(100*f1_values.mean(), 2)) + "%")

2e) Explain what cross_val_score() has done in its first occurrence?

http://scikit-learn.org/stable/modules/generated/sklearn.model_selection.cross_val_score.html

FILES FOR QUESTIONS:

FILE 1: Utilities.py:

import numpy as np import matplotlib.pyplot as plt

def visualize_classifier(classifier, X, y, title=''): # Define the minimum and maximum values for X and Y # that will be used in the mesh grid min_x, max_x = X[:, 0].min() - 1.0, X[:, 0].max() + 1.0 min_y, max_y = X[:, 1].min() - 1.0, X[:, 1].max() + 1.0

# Define the step size to use in plotting the mesh grid mesh_step_size = 0.01

# Define the mesh grid of X and Y values x_vals, y_vals = np.meshgrid(np.arange(min_x, max_x, mesh_step_size), np.arange(min_y, max_y, mesh_step_size))

# Run the classifier on the mesh grid output = classifier.predict(np.c_[x_vals.ravel(), y_vals.ravel()])

# Reshape the output array output = output.reshape(x_vals.shape)

# Create a plot plt.figure()

# Specify the title plt.title(title)

# Choose a color scheme for the plot plt.pcolormesh(x_vals, y_vals, output, cmap=plt.cm.gray)

# Overlay the training points on the plot plt.scatter(X[:, 0], X[:, 1], c=y, s=75, edgecolors='black', linewidth=1, cmap=plt.cm.Paired)

# Specify the boundaries of the plot plt.xlim(x_vals.min(), x_vals.max()) plt.ylim(y_vals.min(), y_vals.max())

# Specify the ticks on the X and Y axes plt.xticks((np.arange(int(X[:, 0].min() - 1), int(X[:, 0].max() + 1), 1.0))) plt.yticks((np.arange(int(X[:, 1].min() - 1), int(X[:, 1].max() + 1), 1.0)))

plt.show()

FILE 2: multivar_data_nb.txt

2.18,0.57,0 4.13,5.12,1 9.87,1.95,2 4.02,-0.8,3 1.18,1.03,0 4.59,5.74,1 8.25,1.3,2 3.91,-0.68,3 0.55,1.26,0 5.64,6.67,1 9.22,1.46,2 4.36,-1.27,3 2.19,2.66,0 4.36,4.86,1 7.4,4.44,2 3.89,0.14,3 1.67,0.81,0 4.97,5.67,1 8.52,2.13,2 5.24,-0.76,3 1.06,2.07,0 5.69,6.08,1 9.52,2.98,2 4.73,-1.71,3 1.64,0.96,0 5.55,5.68,1 8.1,4.26,2 3.82,-1.23,3 1.09,1.4,0 4.83,6.16,1 7.81,1.86,2 4.91,-2.79,3 1.74,0.77,0 5.31,6.61,1 7.24,1.18,2 4.14,-1.36,3 1.12,2.73,0 5.76,4.67,1 9.04,1.63,2 3.89,-2.01,3 0.31,1.5,0 4.14,5.02,1 8.53,2.3,2 4.5,-0.74,3 1.69,1.72,0 4.99,5.01,1 7.93,3.39,2 3.84,-1.55,3 2.37,0.15,0 5.32,5.93,1 7.81,2.63,2 2.64,-0.69,3 0.59,0.67,0 5.54,5.44,1 9.62,4.59,2 3.6,-1.84,3 1.64,0.48,0 5.47,6.16,1 9.53,2.4,2 4.74,-1.74,3 1.96,1.99,0 5.92,6.03,1 7.88,1.71,2 5.39,-2.82,3 0.82,1.96,0 4.5,5.73,1 7.29,1.79,2 3.31,-1.45,3 0.94,2.09,0 5.2,6.15,1 7.98,1.61,2 4.47,-2.51,3 1.31,1.01,0 5.93,7.36,1 8.66,2.31,2 4.92,-1.34,3 -0.39,2.06,0 5.18,6.24,1 5.35,1.36,2 5.25,-0.93,3 1.65,2.26,0 5.74,6.22,1 8.04,1.6,2 4.43,-2.43,3 1.99,1.73,0 4.53,6.67,1 8.57,1.52,2 4.16,-0.22,3 1.5,1.31,0 6.13,6.32,1 10.62,1.67,2 4.92,-1.05,3 0.05,0.38,0 3.84,5.8,1 8.35,2.31,2 3.14,-1.23,3 1.81,1.33,0 2.56,5.91,1 9.02,2.76,2 4.6,-2.16,3 0.33,1.43,0 4.46,4.99,1 8.45,2.15,2 4.95,-2.04,3 0.87,1.53,0 4.81,6.54,1 9.79,2.24,2 3.27,-1.06,3 1.35,2.1,0 4.64,7.8,1 9.5,2.49,2 4.5,0.31,3 1.3,2.01,0 4.02,5.97,1 8.36,1.99,2 4.97,-2.08,3 0.62,1.85,0 5.38,5.19,1 9.05,3.26,2 4.72,-0.14,3 2.91,2.18,0 5.15,5.81,1 8.98,2.76,2 5.2,-1.74,3 0.29,2.09,0 5.73,6.34,1 9.78,2.65,2 4.6,-1.53,3 0.42,1.95,0 3.74,6.49,1 9.31,1.57,2 5.28,-0.33,3 2.2,1.72,0 4.55,5.14,1 7.77,2.17,2 4.43,-2.28,3 -0.04,0.47,0 4.1,6.79,1 8.61,1.64,2 4.22,-0.59,3 1.84,0.95,0 3.55,7.28,1 8.94,3.6,2 4.21,-2.44,3 1.24,3.41,0 5.16,7.36,1 8.93,1.25,2 4.09,-1.41,3 1.57,0.92,0 4.69,4.76,1 8.85,2.18,2 4.43,-0.82,3 0.59,2.13,0 5.84,5.02,1 8.9,3.61,2 4.04,0.71,3 0.01,1.43,0 5.22,6.49,1 8.37,2.41,2 4.95,-1.45,3 1.18,0.53,0 5.63,5.08,1 8.57,1.16,2 4.24,-1.03,3 0.94,1.44,0 5.92,5.07,1 8.85,4.45,2 2.64,-1.79,3 1.44,1.72,0 4.45,6.67,1 8.16,1.76,2 4.5,-2.56,3 1.9,2.23,0 4.92,6.01,1 8.67,2.18,2 4.51,-1.46,3 0.14,0.06,0 5.55,4.9,1 9.27,3.24,2 4.85,-1.07,3 1.52,2.25,0 6.17,5.23,1 7.55,1.92,2 4.72,-1.61,3 2.46,2.01,0 5.24,5.5,1 8.97,2.55,2 5.67,-1.36,3 2.08,3.0,0 5.6,5.93,1 7.48,3.28,2 3.58,-0.23,3 1.99,1.21,0 4.89,7.32,1 8.48,2.36,2 3.36,-0.88,3 1.49,1.44,0 4.97,6.23,1 8.64,2.56,2 4.79,-0.6,3 1.14,1.85,0 4.25,5.36,1 8.01,0.68,2 3.89,-1.53,3 1.31,1.78,0 3.51,6.48,1 7.57,1.73,2 4.38,-2.39,3 1.36,1.52,0 6.32,4.84,1 7.75,2.63,2 4.05,-0.61,3 0.85,0.72,0 3.81,5.92,1 8.46,2.43,2 5.56,-2.22,3 1.19,3.08,0 4.46,6.19,1 7.06,3.23,2 4.74,-1.1,3 2.02,1.86,0 3.66,7.55,1 9.31,2.03,2 5.12,0.46,3 0.16,0.9,0 5.55,6.47,1 7.8,2.97,2 3.26,-1.0,3 0.66,0.52,0 4.54,5.44,1 7.58,3.1,2 3.46,-2.51,3 1.58,1.81,0 5.17,7.57,1 8.27,1.36,2 4.55,-1.21,3 0.35,1.46,0 4.58,4.76,1 9.61,2.32,2 5.8,-1.06,3 1.29,1.56,0 3.8,5.42,1 8.78,1.29,2 4.6,-0.14,3 1.82,0.44,0 3.9,6.53,1 7.96,3.13,2 4.2,-0.62,3 0.98,1.41,0 6.29,5.48,1 9.31,2.93,2 4.1,-0.94,3 0.84,0.06,0 4.41,5.33,1 8.79,3.51,2 4.58,-0.38,3 0.92,1.98,0 5.64,6.38,1 9.24,3.5,2 5.0,-1.76,3 1.19,1.24,0 5.72,5.54,1 8.73,2.47,2 4.52,-1.57,3 1.04,2.23,0 4.4,6.56,1 7.16,2.26,2 4.36,-0.34,3 0.95,2.12,0 6.2,6.39,1 8.12,2.28,2 5.89,-0.95,3 1.3,0.3,0 4.79,6.8,1 9.22,1.75,2 4.46,-0.25,3 1.49,1.32,0 4.07,5.99,1 9.79,0.8,2 4.72,-2.27,3 1.29,0.8,0 3.89,5.92,1 8.11,2.7,2 5.05,-1.11,3 0.28,0.4,0 4.49,5.25,1 9.36,2.33,2 4.62,-1.49,3 1.85,0.23,0 4.34,5.57,1 8.03,1.73,2 4.41,-1.01,3 1.41,0.43,0 5.12,5.84,1 8.12,2.13,2 3.76,-0.81,3 0.32,1.33,0 4.93,6.04,1 7.79,2.02,2 3.88,-1.26,3 0.72,2.35,0 4.87,6.85,1 8.64,2.82,2 3.67,-0.63,3 0.63,1.5,0 5.1,5.33,1 8.01,3.83,2 4.29,-1.0,3 3.13,1.55,0 6.16,5.89,1 7.6,2.88,2 3.98,-0.87,3 1.35,-1.04,0 4.84,6.44,1 8.31,2.57,2 4.6,-2.11,3 1.55,2.11,0 5.86,6.72,1 7.7,2.5,2 4.19,-0.33,3 0.56,2.04,0 3.09,6.27,1 8.32,3.71,2 5.6,-1.68,3 2.21,1.84,0 3.85,7.08,1 7.19,3.13,2 4.82,-1.77,3 1.74,2.53,0 4.88,5.45,1 8.03,1.3,2 3.95,-2.81,3 1.53,2.37,0 5.52,4.55,1 7.97,1.66,2 4.53,-0.93,3 2.19,0.91,0 5.17,5.63,1 8.08,2.72,2 5.32,-0.75,3 1.41,2.47,0 6.33,5.31,1 9.16,2.25,2 4.97,-0.34,3 2.34,1.26,0 6.1,5.49,1 8.62,1.05,2 5.35,-0.09,3 1.77,2.37,0 5.88,6.19,1 9.51,1.51,2 4.68,-0.99,3 1.3,1.85,0 3.96,4.95,1 9.42,2.13,2 4.24,-1.84,3 -0.25,1.85,0 5.04,6.24,1 7.36,2.37,2 4.36,-2.54,3 0.95,2.12,0 4.61,7.16,1 7.89,2.58,2 4.71,-1.98,3 1.6,1.68,0 4.45,4.86,1 8.75,4.27,2 4.46,-0.21,3 0.68,1.89,0 4.5,5.32,1 8.46,3.73,2 4.68,-2.03,3 0.43,1.23,0 7.1,6.16,1 8.92,2.65,2 4.31,-1.96,3 0.01,0.19,0 5.55,3.53,1 7.71,1.47,2 4.63,-1.4,3 1.2,-0.17,0 5.16,6.5,1 9.04,2.81,2 4.17,-0.5,3 1.75,1.09,0 4.55,7.6,1 8.81,2.94,2 3.08,-0.92,3 1.22,1.07,0 5.4,6.44,1 8.09,2.02,2 6.2,-0.72,3 0.69,1.63,0 4.01,6.83,1 7.3,0.73,2 3.29,-0.3,3 0.55,0.7,0 4.4,6.75,1 8.71,3.38,2 6.12,-1.8,3